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Monrad.410.04_bivariate - M Z W Z m gmwmé{SWAMA Mc/Wfld...

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Unformatted text preview: M Z W Z m gmwmé {SWAMA Mc/Wfld ZUZM/MLHM L076 (1 b C 0‘ 16 am we be Camsbmh . 5 PW" [41A ‘9 X and \f/ [MK 4 53' °d a}. WshxbuRom WWL Mia/ms #1 mm L mi Wax/mow of and d: J MAPCC/fve/ZJ . TM , COFFQ‘OkhOt/l COETCROEGML F.) k :3 a) Imem‘ flaw/hm 0 X; J Y = xx: P“ 3f“0<“/*‘«> c mdomjc oflghfi'bu‘iom K XXSCMQEEJ <H’WLIKS) a“ gioggakm‘hons (98:38 {3“ 0m 0x (Me (hmP‘Me. Inc Hi {MT me X am Y/ Mm HQ my w 45“ m m; (3.5m 0 d4 1. (>5 0 _.... X20110“ A0 “0‘ Sl’flb «om 0‘2 63 mama/Q «fiv‘fi meat/1 H k (\l 4. ”0 9p A >2 I \5 \./ am .! Wat/me (I ~— pl) d: , (Emma (35.23)) X MM Y WLL (HOLLPWAWL i? and 0M3 }‘€ 10:0 SUNS HEIGHT IN INCHES Scatter diagram for the heights of 1078 fathers and their sons, based on Pearson‘s data. There is a positive association between the heights of the fathers and sons. The dots in the vertical strip over 72" represent all the father—son pairs where the father is 6' tall, to the nearest'inch. .The average height of the corresponding sons is about 71". Similarly, the average heights of the sons of the 6A" fathers is about 67“. An 8" increase in fathers' heights (from 6M" to 72") is associated with a 4" increase in sons‘ heights, on the average. Each one-inch in- crease in fathers' heights is associated with a half—inch increase in their sons‘ heights, on the average. The association is bound to be fairly weak, because there is so much variability in the heights of the sons even after fixing their father‘s height. For instance, the sons of the 6‘ fathers show almost as much variability in height as do all the sons together. 60 62 61 66 66 7D 72 71 76 78 FRTHERS HEIGHT IN INCHES 80 THE CORRELATION COEFFICIENT The correlation coefficient—six positive values. The dia- grams are scaled so that the average equals 3 and the SD equals 1, hori- zontally and vertically; there are 50 points in each diagram. Clustering is measured by the correlation coefficient. CORR COEFF IS 0.00 CORR COEFF IS 0.40 6 - 6 _, 5 — 5 1 4 — 4 1 c ’ l 3 - 3 1 ' 2 — 2 1 1 — 1 1 O -1 r l I I l '1 O 1—‘*"1—-—r——r———r—-——~r% o 1 2 3 4 5 6 o 1 2 3 4 5 6 CORR COEFF IS 0.60 CORR COEFF Is 0.80 6 - 6 _ 5 l 5 - 41 4 J I '- 3 ‘1 . 3 J 2 1 2 1 " 1 - 3 1 _ 0 1—" I I I" I 'T" I O T—‘fir—I——T"’—"—l—r—_} o 1 2 3 4 5 6 o 1 2 3 4 5 6 CORR COEFF IS 0.90 CORR COEFF Is 0.95 6 6 l l 5 1 5 — 4 — 4 - 3 sl . 2 - 1 - 2 1 - ’ 11 . 11 , 0‘]- ”"T—"“ 'l l' —l l '—I 0 4*—r—-—r—I——'—1—r——1 o 1 2 3 4 5 6 o 1 2 3 4 5 6 U1 4:. CO The correlation coefficient—six negative values. The dia- grams are scaled so the average equals 3 and the SD equals 1, horizontally and vertically; there are 50 points in each diagram. Clustering is measured by the correlation coefficient. CORR COEFF IS -0.30 CORR COEFF IS -O.50 fl 6 — —I 5 1 J 4 J - 3 J . o I I _ 2 _ _. 1 ._ 1 I I I I I l O ‘I I l I ‘l‘ 1 0 1 2 3 4 5 6 O 1 2 3 4 6 CORR COEFF IS —0.7O CORR COEFF IS —O.90 6 _ I . I 5 I o . I o I . . 44 .. . - I . _ 3] ‘.‘ I ' . ' 2J '- . 1 I 1 I . ’l _-l‘_ I" | r—— I I OJ l 7—.- I 'T‘" "I 0 1 2 3 4 5 6 0 1 2 4 6 CORR COEFF IS -O.95 CORR COEFF IS -0.99 Bl 51 . . 4 - 3.“ .0 (D ...
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